Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body

Polygons Inscribed in a Convex Figure

“…It is proved in [6, 7] that each convex figure is circumscribed about an affine image of a regular pentagon (an affine-regular pentagon) with vertex at a prescribed boundary point of the figure. The same is proved in [8] for an arbitrary convex pentagon P such that the sum of any two neighboring angles of P is greater than π.It is proved in [2] that each convex figure is circumscribed about an affine image of a regular hexagon, and the same is proved in [13,14] for an arbitrary centrally symmetric convex hexagon.It is proved in [7] that each centrally symmetric convex figure is circumscribed about an affine image of the regular octagon, and the same is proved in [12] for the centrally symmetric octagon with vertices at the vertices of the regular decagon. …”

“…It is proved in [7] that each centrally symmetric convex figure is circumscribed about an affine image of the regular octagon, and the same is proved in [12] for the centrally symmetric octagon with vertices at the vertices of the regular decagon.…”